Now that Uncertainty Wednesday has covered the various ways in which our ability to observe reality are limited, we will look at limitations on explanations. Again for those readers just starting this series, the basic framework has uncertainty resulting from limits on observations and explanations of reality. Now today’s post isn’t titled “Limits on Explanations” but just “Explanations.” The reason for that is that I think I need to first explain what an explanation is (in retrospect I should have maybe done this for observations as well but last week’s post gets to the heart of that: observation is an information transfer from reality to the observer and hence are a physical process themselves).

OK, so what is an explanation? An explanation is a relational story about reality. Let’s unpack this starting with the “about reality” part. We have lots of stories in the world that are about fictional universes. Those are not explanations. Take the Harry Potter series for example. Even though it contains detailed “explanations” of say the game of Quidditch or the construction of Horcruxes, these are not explanations in the sense used here. Why? Because there is no corresponding observable reality. And in the absence of a corresponding observable reality, the story can be changed as pleases the author (or reader, or movie maker). You can still compare one version of a fictional story against another or examine a fictional story for internal consistency, but you can never have any corresponding observations because there is no underlying reality.

The second important qualifier for explanations is that they must be relational stories. Saying “The Earth is round” is not an explanation. It is simply a description, which is the same as a “possible” observation. I say “possible” because there are many descriptions we can come up with of reality that are different from what is observed (eg “The Earth is flat”). Saying “The Earth revolves around the Sun” is an explanation. It establishes a relationship between the Earth and the Sun. And if I switch it around to “The Sun revolves around the Earth” I get a different explanation. Changing an explanation in this way has implications for what should be observed which is why relational stories about reality cannot be changed simply at the whim of the author.

The relational nature of explanations can be seen in our ability to express many of them as mathematical equations (equalities or inequalities) with at least two variables. The equation expresses the relationship between the two. We can also see that an equation with only one variable, something like x = 42 expresses a description, not an explanation.

There is much much more to be said about explanations, such as where they come from, what makes for a good explanation and how explanations relate to observations. Over time I am planning to get to all of those but in the next few posts we will look at limits on explanations.

PS My thinking on explanations is heavily inspired by David Deutsch’s writing, in particular “The Beginning of Infinity” which has as its subtitle “Explanations that Transform the World.”